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Questions and Answers
What is the value of x in the equation $-(1 - x) = -2(3x - 1)$?
What is the value of x in the equation $-(1 - x) = -2(3x - 1)$?
If $-5x + 7 = 2x - 3$, what is the value of x?
If $-5x + 7 = 2x - 3$, what is the value of x?
What is the solution for n in the inequality $-17 + 3n ≤ 7(n - 2)$?
What is the solution for n in the inequality $-17 + 3n ≤ 7(n - 2)$?
Which point is on the graph of $2x - 16y = 8$?
Which point is on the graph of $2x - 16y = 8$?
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Solving the area formula $A = 1/2 (b₁ + b₂)h$ for $b₁$ results in which equation?
Solving the area formula $A = 1/2 (b₁ + b₂)h$ for $b₁$ results in which equation?
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From the profit equation $P = 2n - 800$, express n as a function of P.
From the profit equation $P = 2n - 800$, express n as a function of P.
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Which inequality could be used to determine b, the number of blouses, and p, the number of pants that Grace can afford?
Which inequality could be used to determine b, the number of blouses, and p, the number of pants that Grace can afford?
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In the given right triangle, which system of equations could be used to solve for x and y if y is 15 less than twice x?
In the given right triangle, which system of equations could be used to solve for x and y if y is 15 less than twice x?
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What is the maximum number of hamburgers Harry can buy if he buys 20 hot dogs?
What is the maximum number of hamburgers Harry can buy if he buys 20 hot dogs?
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Which of the following represents a function based on the given set of ordered pairs?
Which of the following represents a function based on the given set of ordered pairs?
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What is the range of the function represented by the given temperature vs. time graph?
What is the range of the function represented by the given temperature vs. time graph?
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Based on the graph modeling price markup, which option correctly describes the function's domain?
Based on the graph modeling price markup, which option correctly describes the function's domain?
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What is the total bill a homeowner must pay for using 3800 gallons of water, considering both water and sewer fees?
What is the total bill a homeowner must pay for using 3800 gallons of water, considering both water and sewer fees?
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What is the weight of a baby at age 5 months according to the function f(x) = 1.5x + 7?
What is the weight of a baby at age 5 months according to the function f(x) = 1.5x + 7?
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What is the value of the function f(x) = 5(x + 1) + 2x at x = 3?
What is the value of the function f(x) = 5(x + 1) + 2x at x = 3?
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Which of the following pairs represents a function based on the given criteria?
Which of the following pairs represents a function based on the given criteria?
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What is the correct domain for the profit function P(t) of the math club selling T-shirts, where each T-shirt sold represents a profit of $2?
What is the correct domain for the profit function P(t) of the math club selling T-shirts, where each T-shirt sold represents a profit of $2?
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In the context of the lava flow modeled by the function f(d) = 800d, what is the best description of the domain?
In the context of the lava flow modeled by the function f(d) = 800d, what is the best description of the domain?
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What does an average change in distance of zero imply about Victoria's movements between 10:00 a.m. and 11:00 a.m.?
What does an average change in distance of zero imply about Victoria's movements between 10:00 a.m. and 11:00 a.m.?
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How is the average rate of change for the function f(x) calculated over the interval [1, 8] given specific values?
How is the average rate of change for the function f(x) calculated over the interval [1, 8] given specific values?
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When calculating the average rate of change in miles per gallon from 180 miles to 480 miles, which values are used in the expression?
When calculating the average rate of change in miles per gallon from 180 miles to 480 miles, which values are used in the expression?
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Which of the following statements about the distance and time table for Victoria is accurate?
Which of the following statements about the distance and time table for Victoria is accurate?
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What does the slope of the line represented in the graph from (0,0) to (5,5) signify?
What does the slope of the line represented in the graph from (0,0) to (5,5) signify?
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Which range of values can correctly be described as the domain of the function P(t), where t represents the number of T-shirts sold?
Which range of values can correctly be described as the domain of the function P(t), where t represents the number of T-shirts sold?
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Study Notes
Solving Equations and Inequalities
- Question 1: The value of x in the equation -(1 - x) = -2(3x - 1) is 1/7.
- Question 2: If -5x + 7 = 2x - 3, then x = 10/7.
- Question 3: The solution for n in the inequality -17 + 3n ≤ 7(n - 2) is n ≥ 15/4*.
- Question 4: The point (1/2, 0) is on the graph of 2x -16y = 8.
Trapezoids and Formulas
- Question 5: The formula A = 1/2 (b₁ + b₂)h can be used to determine the area of a trapezoid. Solving for b₁ will result in the equation b₁ = 2A/h - b₂.
- Question 6: The equation P = 2n - 800 can be rearranged to solve for n as a function of P resulting in the following: n = 1/2 (P + 800)
- Question 7: The formula C = (5n + 40)/9 can be rearranged to solve for the number of chirps as a function of the temperature in degrees Celsius. The correctly rearranged formula is n = 9/5 (C - 40)*.
Inequalities and Systems of Equations
- Question 8: The inequality 17b + 25p ≤ 75 could be used to determine b, the number of blouses, and p, the number of pants Grace can afford.
- Question 9: The system of equations x + y = 90* and 2x - y = 15 could be used to solve for x and y.
Word Problems
- Question 10: A possible way Harry might buy the hamburgers and hot dogs is 66 hamburgers and 33 hot dogs.
- Question 11: The set of ordered pairs {(-4, 4), (-2, 4), (1, 4), (5, 4)} represents a function.
Functions
- Question 12: The range of the function shown in the graph is All real numbers between and including 50 and 212.
- Question 13: Based on the given graph, the function's domain is Numbers between and including 0 and 30.
- Question 14: The total amount a homeowner will pay if the water and sewer usage for one month is 3800 gallons is $43.35.
- Question 15: According to the model f(x) = 1.5x + 7, the weight of a baby at age 5 months is 14.5 pounds.
- Question 16: Given f(x) = 5(x + 1) + 2x, f(3) is 26.
- Question 17: The domain of the function shown in the graph is All real numbers between 0 and 6.
- Question 18: A reasonable domain of the function P(t) is 0 ≤ t ≤ 500.
- Question 19: The domain of f(d) in the context of the lava flow is best described as All non-negative integers.
- Question 20: The best interpretation of Victoria's average change in distance during this time is Victoria could have stayed at the same location from 10:00 a.m. to 11:00 a.m..
Rate of Change
- Question 21: The average rate of change for the function f(x) over the interval [1, 8] is 4.
- Question 22: The average rate of change, in miles per gallon, from 180 miles to 480 miles is 480 - 180 / 300.
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Description
This quiz focuses on solving equations and inequalities, including their graphical interpretations and applications in trapezoid area calculations. Test your skills with varied problems, ranging from basic equations to more complex algebraic manipulations.
